How to Calculate P Value from F

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The F distribution is a ratio of two chi-square statistics, each divided by their respective degrees of freedom. If the degrees of freedom of a test statistic (statistic derived from data points) are given, then finding whether the corresponding p-value falls outside of the critical p-value is a matter of using a distribution table. If an exact p-value is needed, a spreadsheet can give it. If the degrees of freedom are not given, they can be determined from a count of data points and variables.

Things You'll Need

  • F-distribution table
  • Observed F statistic
  • Spreadsheet (optional)

Determine Degrees of Freedom

  • Determine the degrees of freedom from the given F distribution. If you are given the F distribution that the observed F-value follows, the notation will read ~F(X,Y). X is the degrees of freedom of the chi-square distribution in the numerator. Y is the degrees of freedom for the denominator.

  • Go back to the calculation of the observed F value to see what the chi-square statistics were divided by, if the above does not work.

  • Use the equations p - k and n - p - 1 to solve for the degrees of freedom, if the above did not work. These equations apply if the F test is being used as a test on the explanatory power of additional variables.

    n refers to the total number of data points.
    p refers to the total number of variables in the full model.
    k refers to the number of variables of the full model contained in the partial model, i.e., the number of variables added to test their explanatory power.

  • Subtract 1 from each of the observation counts of the two normal population samples, if the F test is instead being used to test the difference in variance between normal distributions. These will be the corresponding degrees of freedom of the two samples, and therefore of the two chi-square statistics.

Use Table

  • Look up an F-distribution table. One is available at the Image Shack link in the references.

  • Find the appropriate degrees of freedom in the table. Note that if you are given that the observed F ~ F(X,Y), then the X is the degree of freedom corresponding to the numerator, and is therefore found by column. Y is found by row.

  • Find the critical p-value you were given in the correct row. For example, in the Image Shack table, the column A corresponds to the p-values.

  • Determine the F-value for this p-value/degree-of-freedom combination.

  • Reject the null hypothesis if the observed F is greater than the critical F value.

  • Use a spreadsheet, if an exact p-value is needed for the observed F statistic. In Excel the syntax is "=FDIST(W,X,Y)" where we continue with our prior notation of the numerator and denominator degrees of freedom as X and Y. W refers to the observed F value.

References

  • Probability and Statistics; Morris H. DeGroot; 1985
  • Mathematical Statistics; John E. Freund; 1992
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